How does electromagnetic radiation differ from nuclear radiation?

Electromagnetic radiation is concerned with the movement of photons (individual, discrete 'packets' of light energy.) The frequency of electromagnetic radiation is directly proportional to its energy and inversely proportional to it's wavelength. Thus, a higher frequency will mean that the photons have a shorter wavelength and have more energy.

Different frequencies, and therefore energies, of electromagnetic radiation will give it different properties. Because of this, the frequencies of electromagnetic radiation are divided into a spectrum based on the different properties of electromagnetic radiation of different frequencies. This spectrum goes from radio waves at the very low end to gamma rays at the other end.

See the link at the bottom for a diagram of the Electromagnetic Spectrum.
However, in the below image the word 'heat' is wrong. Between Infra-red and Radio waves are microwaves.

Nuclear radiation is normally concerned with any form of radiation emitted as a result of radioactive decay, in which a large, unstable nucleus of an atom breaks down to form a more stable one.

There are three types of nuclear radiation: alpha, beta, and gamma. Alpha decay is when an unstable nucleus emits an alpha particle which is composed of two protons and two neutrons; i.e. it is effectively a helium nucleus. Beta decay is when an unstable nucleus emits a beta particle (an electron), and gamma emission is when an unstable nucleus emits high energy electromagnetic radiation called gamma rays.